What is the integral from 1 to 3 of 2x^2-3x+5 ?

The integral from 1 to 3 of 2x^2-3x+5 is 46/3

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integral from 1 to 3 of 2x^2-3x+5

\int_{1}^{3} 2 x^{2} - 3 x + 5 d x

\frac{46}{3}

Solution steps

\int_{1}^{3} 2 x^{2} - 3 x + 5 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{1}^{3} 2 x^{2} d x - \int_{1}^{3} 3 x d x + \int_{1}^{3} 5 d x

\int_{1}^{3} 2 x^{2} d x = \frac{52}{3}

\int_{1}^{3} 3 x d x = 12

\int_{1}^{3} 5 d x = 10

= \frac{52}{3} - 12 + 10

Simplify

\frac{52}{3} - 12 + 10 : \frac{46}{3}

= \frac{46}{3}

\int_{- 1}^{1} cos (2 x) d x

\int_{1}^{2} 5 x (x^{2} + 1) d x

\int_{0}^{3} 10 e^{2 x} d x

\int_{0}^{1} \frac{x - 1}{x ^{2} - 2 x + 3} d x

\int_{4}^{t} \frac{12}{x} d x

What is the integral from 1 to 3 of 2x^2-3x+5 ?
The integral from 1 to 3 of 2x^2-3x+5 is 46/3